Faraday’s law of induction/ презентация

to a sensitive ammeter, the ammeter shows that a current is induced in the loop.

When the magnet is held stationary, there is no induced current in the loop, even when the magnet is inside the loop.

When the magnet is moved away from the loop, the ammeter deflects in the opposite direction, indicating that the induced current is opposite that shown in part (a).

the magnet is moving relative to it and we relate this detection to a change in magnetic field.
Thus, it shows that a relationship exists between current and changing magnetic field.
So a current is set up even though no batteries are present in the circuit! We call such a current an induced current and say that it is produced by an induced emf.

the ammeter. The same is when the switch is closed ammeter detects no current.
When the switch in the primary circuit is either opened or thrown closed. At the instant the switch is closed, the galvanometer needle deflects in one direction and then returns to zero. At the instant the switch is opened, the needle deflects in the opposite direction and again returns to zero.

current in the primary circuit creates changing magnetic field in the iron ring, which creates current in the secondary coil.
When the switch was closed, and is opened, the current in the primary circuit also is changing – from some constant value to zero, it creates changing magnetic field in the iron ring, which creates current in the secondary coil.

changing magnetic field. The induced current exists only while the magnetic field through the secondary coil is changing. Once the magnetic field reaches a steady value, the current in the coil disappears.

Summary of the two experiments

proportional to the time rate of change of the magnetic flux through the circuit.



Here ФB is the magnetic flux through the circuit:

area A in the presence of a uniform magnetic field B. The angle between B and the normal to the loop is Θ.
ΦB=BAcosΘ
An emf can be induced in the circuit in several ways:

The magnitude of B can change with time.
The area enclosed by the loop can change with time.
The angle Θ between B and the normal to the loop can change with time.
Any combination of the above can occur.

change in flux have opposite algebraic signs. This has a very real physical interpretation that has come to be known as Lenz’s law (2 equivalent variants):
The induced current in a loop is in the direction that creates a magnetic field that opposes the change in magnetic flux through the area enclosed by the loop.
Induced currents produce magnetic fields which tend to cancel the flux changes that induce them.

loop, a current is induced in the direction shown. The magnetic field lines shown belong to the bar magnet.

Picture (b): his induced current produces its own magnetic field directed to the left that counteracts the increasing external flux. The magnetic field lines shown are those due to the induced current in the ring.

the magnetic flux due to the external magnetic field, through the area enclosed by the loop, increases in time. By Lenz’s law, the induced current must be counterclockwise so as to produce a counteracting magnetic field directed out of the page.

a uniform magnetic field perpendicular to the plane of the loop. If B changes in time, an electric field is induced in a direction tangent to the circumference of the loop.

charge q once around the loop is equal to qε. Because the electric force acting on the charge is qE, the work done by the electric field in moving the charge once around the loop is qE(2πr):

is integration along an enclosed path.
ФB is a magnetic flux through that enclosed path (along which the integration goes).
The induced electric field E in this expression is a nonconservative field that is generated by a changing magnetic field.

of metal moving through a magnetic field.
Eddy currents are used in many braking systems of subway and rapid-transit cars.
Eddy currents are often undesirable because they represent a transformation of mechanical energy to internal energy. To reduce this energy loss, conducting parts are often laminated—that is, they are built up in thin layers separated by a nonconducting material. This layered structure increases the resistance of eddy current paths and effectively confines the currents to individual layers.

magnetic field. As the plate enters or leaves the field, the changing magnetic flux induces an emf, which causes eddy currents in the plate.

currents are counterclockwise. As the plate leaves the field (position 2), the currents are clockwise. In either case, the force on the plate is opposite the velocity, and eventually the plate comes to rest.

When slots are cut in the conducting plate, the eddy currents and retarding force are reduced and the plate swings more freely through the magnetic field.

absence of any dielectric or magnetic material:

(1)


(2)


(3)


(4)

charge inside it.
This is the Gauss’s law: the total electric flux through any closed surface equals the net charge inside that surface divided by ε0.
This law relates an electric field to the charge distribution that creates it.

as Gauss’s law in magnetism, states that the net magnetic flux through a closed surface is zero.
That is, the number of magnetic field lines that enter a closed volume must equal the number that leave that volume. This implies that magnetic field lines cannot begin or end at any point. It means that there is no isolated magnetic monopoles exist in nature.

magnetic flux through that enclosed path.
This equation is Faraday’s law of induction, which describes the creation of an electric field by a changing magnetic flux.
This law states that the emf, which is the line integral of the electric field around any closed path, equals the rate of change of magnetic flux through any surface area bounded by that path.

law. It describes the creation of a magnetic field by an electric field and electric currents: the line integral of the magnetic field around any closed path is the sum of μ0 times the net current through that path and ε0μ0 times the rate of change of electric flux through any surface bounded by that path.

absence of the term for magnetic monopoles in Equation (2).
Equations (3) and (4) are symmetric in that the line integrals of E and B around a closed path are related to the rate of change of magnetic flux and electric flux, respectively.
Maxwell’s equations are of fundamental importance not only to electromagnetism but to all of science.

electric and magnetic fields), which travel with a speed

the speed of light. Furthermore, the theory shows that such waves are radiated by accelerating charges.

of free space:
Magnetic permeability
of free space: